# Disk rotating problem. , help pls

#### makeAwish

Disk rotating problem. urgent, help pls..

Homework Statement

A disk of radius 30.0cm is free to turn about an axle perpendicular to it through its center. It has very thin but strong string wrapped around its rim, and the string is attached to a ball that is pulled tangentially away from the rim of the disk. The pull increases in magnitude and produces an acceleration of the ball that obeys the equation a(t) = At , where t is in seconds and A is a constant. The cylinder starts from rest, and at the end of the third second, the ball's acceleration is 1.50 m/s^2.

a. Express the angular acceleration of the disk as a function of time.

b. How much time after the disk has begun to turn does it reach an angular speed of 17.5 rad/s?
c. Through what angle has the disk turned just as it reaches 17.5 rad/s?

The attempt at a solution

I have found A to be 0.500m/s^3.

but i duno how to do part a.

can help me pls?
thanks!!

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#### makeAwish

Re: Disk rotating problem. urgent, help pls..

i tried applying angular acceleration, alpha = r/a where a is tangential acceleration. and i get 0.3/(0.5t)

the answer shld be in (rad/s^3)t units. and is independent on t..

Last edited:

#### tiny-tim

Homework Helper
Hi janettaywx!

(have an alpha: α )
A disk of radius 30.0cm is free to turn about an axle perpendicular to it through its center. It has very thin but strong string wrapped around its rim, and the string is attached to a ball that is pulled tangentially away from the rim of the disk. The pull increases in magnitude and produces an acceleration of the ball that obeys the equation a(t) = At , where t is in seconds and A is a constant. The cylinder starts from rest, and at the end of the third second, the ball's acceleration is 1.50 m/s^2.

a. Express the angular acceleration of the disk as a function of time.

I have found A to be 0.500m/s^3.
No, A = 0.500m/s
i tried applying angular acceleration, alpha = r/a where a is tangential acceleration. and i get 0.3/(0.5t)

the answer shld be in (rad/s^3)t units. and is independent on t..
No, look at the dimensions …

angular acceleration (α) is in rad/s2,

and ordinary acceleration (a) is in m/s2,

and r is in m,

so a = rα, and α = a/r

#### makeAwish

Re: Disk rotating problem. urgent, help pls..

hahah. thanks for the alpha.

hmm. but i tot A is accel divide by time.. so its units is rad/s³?

so α = 0.5t/0.3 ?

#### makeAwish

Re: Disk rotating problem. urgent, help pls..

hmm.. it shld be indpt of t.. what shld i do next?

#### tiny-tim

Homework Helper
hmm. but i tot A is accel divide by time.. so its units is rad/s³?

so α = 0.5t/0.3 ?
sorry, I misread it … you're right, it is m/s3
hmm.. it shld be indpt of t..
No, α = 0.5t/0.3 is ok … it should be a function of t

(because a = At, and α = a/r, so α = At/r )

#### makeAwish

Re: Disk rotating problem. urgent, help pls..

hmm. say i want to convert it to radians, is this how we convert?

1 rev = 2∏r = 2∏(0.3m)

den 0.5 m/s^3 = 0.5*(1/0.3) rad/s^3?

#### makeAwish

Re: Disk rotating problem. urgent, help pls..

actually, from my qns here, they sae we shld get an answer indpt of t. but i dont rly noe why cos' it is a function of t...

#### tiny-tim

Homework Helper
hmm. say i want to convert it to radians
(why ∏? everyone uses π )

the radian is defined specially so that α = a/r (or ω = v/r) works without adjustment.

#### makeAwish

Re: Disk rotating problem. urgent, help pls..

i see. okay thanks!

#### makeAwish

Re: Disk rotating problem. urgent, help pls..

but how u do 2nd part?? to find the time.

i tried taking time = angular speed / angular accel = 10.5s
but wrong..

#### tiny-tim

Homework Helper
Hi janettaywx!

You have angular acceleration as a function of time …

inegrate it to get angular speed as a function of time

#### makeAwish

Re: Disk rotating problem. urgent, help pls..

Hi janettaywx!

You have angular acceleration as a function of time …

inegrate it to get angular speed as a function of time
hi!!

means i will get (1.67t^2) / 2 = 17.5
so t = 4.58s?

#### makeAwish

Re: Disk rotating problem. urgent, help pls..

ok i got it. thanks a lot!!

Homework Helper

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